I basically agree with Neco. You want a full shoulder turn and you need to make sure you set your wrists relatively early in order to maintain a proper angle throughout your downswing.
However, I wouldn't go as far as saying 'completely stiff'. You still need to be comfortable and be loose. Its the right idea, but i think a better thought is keeping it relatively straight. 'Completely stiff' brings to mind rigidity and .....stiffness. You still want to remain athletic with your swing.
In terms of the gym and all of that....it isn't necessarily too early to start lifting weights. However, its imperative that you talk it over with your doctor, and it is basically a must that you are constantly monitored by a professional (i.e an accredited trainer). Advice from a buddy or just picking up a routine that you've researched online isn't enough. At your age, it is very very easy to get hurt. It doesn't matter if your friends or teammates are whatever are going at it alone, again...you can create damage before you even realize what has happened and get seriously injured.
And as others have stated, this is a perfect time to practice your short game. Amateurs frequently spend relatively too much time working on their long games anyways. You'll eventually likely get bigger and stronger and hit the ball further. For now, keep it in the fairway and work on your game from 50 yards and in.